Carrierless amplitude and phase (CAP) modulation is a coding technique based on quadrature amplitude modulation. In accordance with CAP, an impulse is generated which has two components, an in-phase signal and a corresponding quadrature signal. Each component may have an amplitude, which is equal to one of N different amplitude levels. By combining the two components, an impulse may be generated which has N2 unique combinations of in-phase signal amplitude and quadrature signal amplitude.
FIG. 1 depicts a high level block diagram of a known CAP transmitter front end. Specifically, the CAP transmitter front end system 100 of FIG. 1 comprises a bit-to-symbol mapper 110, a differential encoder 120, a constellation mapper 130, an in-phase filter 140, a quadrature filter 150, a combiner 160 and an analog front end (AFE) 170. The cap transmitter front end 100 of FIG. 1 processes an input bit stream to produce a modulated transmission signal suitable for use by a transmitter back end (not shown).
The bit-to-symbol mapper 110 maps data words within the input bitstream to respective symbols. The differential encoder 120 differentially encodes the symbols. The constellation mapper 130 maps the differentially encoded symbols to a carrierless amplitude and phase (CAP) constellation. The constellation mapper 130 generates two orthogonal signals; namely, in-phase impulse component I and quadrature impulse component Q which together convey the information necessary to define the mapped symbols.
The in-phase filter 140 and quadrature filter 150 provide pulse shaping and passband modulation of, respectively, the in-phase I and quadrature Q impulse signals. The output of the filters 140 and 150 is then subtracted (or combined) by combiner 160 to form a modulated signal, that is processed by a digital-to-analog (D/A) converter (not shown) and other circuitry within the analog front and 170. It is noted that the D/A converter operates a sampling rate of 1/T′=i/T (where i is a suitable integer and 1/T is the symbol rate). The analog signal (Transmit Signal) obtained at the output of the AFE 170 is described by the following equation:
                              s          ⁡                      (            t            )                          =                              ∑                          n              =                              -                ∞                                                    n              =              ∞                                ⁢                      [                                                            a                  n                                ⁢                                                      p                    in                                    ⁡                                      (                                          t                      -                      nT                                        )                                                              -                                                b                  n                                ⁢                                                      p                    qd                                    ⁡                                      (                                          t                      -                      nT                                        )                                                                        ]                                              (                  eq          .                                          ⁢          1                )            
To obtain the output signal s(t), the in-phase 140 and quadrature 150 filters operate upon the upsampled input data by a factor of i. As known to those skilled in the art, upsampling of the input data may occur prior to filtering or within the filtering structure itself. The output of each of these N tap filters at the sampling rate is represented in equation (2) and (3) as follows.
                              FOUT          inphase                =                              ∑                          k              =              0                                      N              -              1                                ⁢                                    a              n                        ⁢                                          p                in                            ⁡                              (                                  t                  -                  kT                                )                                                                        (                  eq          .                                          ⁢          2                )                                          FOUT          quadrature                =                              ∑                          k              =              0                                      N              -              1                                ⁢                                    b              n                        ⁢                                          p                qd                            ⁡                              (                                  t                  -                  kT                                )                                                                        (                  eq          .                                          ⁢          3                )            
Thus, to compute the filtered output for each given input sample for an N tap filter requires N multiplications and N−1 additions. The input to each of the filters for an M ary signal is ±(2p−1) for p=1 . . . M/2. Therefore the levels L=±1, ±3, ±5 . . . ±(2p−1). Unfortunately, such processing by the in-phase filter 140 and quadrature filter 150 requires significant processing power to achieve the large number of multiplication operations per relevant time period.